Integration pointwise pollution error estimates in the finite element method in one dimension

Tsamasphyros, G; Markolefas, S

dc.contributor.author	Tsamasphyros, G	en
dc.contributor.author	Markolefas, S	en
dc.date.accessioned	2014-03-01T01:20:38Z
dc.date.available	2014-03-01T01:20:38Z
dc.date.issued	2004	en
dc.identifier.issn	0168-9274	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16000
dc.subject	Finite elements	en
dc.subject	Inf-sup condition	en
dc.subject	Numerical integration	en
dc.subject	Pointwise pollution error	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Approximation theory	en
dc.subject.other	Estimation	en
dc.subject.other	Galerkin methods	en
dc.subject.other	Integration	en
dc.subject.other	Measurement errors	en
dc.subject.other	Perturbation techniques	en
dc.subject.other	Problem solving	en
dc.subject.other	Vectors	en
dc.subject.other	Gauss quadrature	en
dc.subject.other	Inf-sup conditions	en
dc.subject.other	Pointwise pollution errors	en
dc.subject.other	Shape functions	en
dc.subject.other	Finite element method	en
dc.title	Integration pointwise pollution error estimates in the finite element method in one dimension	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.apnum.2004.01.012	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.apnum.2004.01.012	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	An a priori estimate for the pointwise pollution effect caused by the approximate integration is given. Furthermore, a bound for the integration perturbation error in the H-1 norm is derived, for general problems satisfying the inf-sup stability condition and quasi-uniform h-extension meshes. In the numerical studies a problem with singular exact solution is discussed. The example aims at exploring how the pollution (from the numerical integration of the singular force vector), influences the accuracy and the rates of convergence (of both h- and p-versions) of the finite element method. Finally, for the purpose of verification of the pointwise pollution error estimate, numerical results from two additional problems with smooth exact solutions are presented. (C) 2004 IMACS. Published by Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Applied Numerical Mathematics	en
dc.identifier.doi	10.1016/j.apnum.2004.01.012	en
dc.identifier.isi	ISI:000224593300013	en
dc.identifier.volume	51	en
dc.identifier.issue	2-3	en
dc.identifier.spage	345	en
dc.identifier.epage	360	en